GATE EC 2022 Set 1 — Question 62
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Communications → Error Control Coding → Binary Symmetric Channel
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Question
Consider communication over a memoryless binary symmetric channel using a Hamming code. Each transmitted bit is received correctly with probability , and flipped with probability . For each codeword transmission, the receiver performs minimum Hamming distance decoding, and correctly decodes the message bits if and only if the channel introduces at most one bit error.For , the probability that a transmitted codeword is decoded correctly is _________ (rounded off to two decimal places).
Correct answer
0.84 to 0.86
Solution
For a Hamming code, the total number of bits in a codeword is . This specific Hamming code can correct up to error. Given:
- Probability of bit error
- Probability of correct bit reception
1.Probability of 0 errors:
2.Probability of 1 error:
Total probability of correct decoding:Rounding to two decimal places, we get .Continue learning with Success Tracker
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